Computational intelligence for studies on genetic diversity between genotypes of biomass sorghum

The objective of this work was to evaluate the potential of computational intelligence and canonical variables for studies on the genetic diversity between biomass sorghum (Sorghum bicolor) genotypes. The experiments were carried out in the experimental field of Embrapa Milho e Sorgo, in the municipalities of Nova Porteirinha and Sete Lagoas, in the state of Minas Gerais, Brazil. The following traits were evaluated: days to flowering, plant height, fresh biomass yield, total dry biomass, and dry biomass yield. The study of genetic diversity was performed through the analysis of canonical variables. For the recognition of the organization pattern of genetic diversity, Kohonen’s self-organizing map was used. The use of canonical variables and a self-organizing map were efficient for the study of genetic diversity. The application of computational intelligence using a self-organized map is promising and efficient for studies on the genetic diversity between biomass sorghum genotypes.

Index terms:
Sorghum bicolor; canonical variables; Kohonen’s self-organized map

Authorship

Michele Jorge da Silva ^**Corresponding author: michelejorgesilva@gmail.com

Universidade Federal de Viçosa, Departamento de Biologia Geral, Avenida Peter Henry Rolfs, s/no, Campus Universitário, CEP 36570-000 Viçosa, MG, Brazil. E-mail: michelejorgesilva@gmail.com, antonio.silva.c.junior@gmail.com, cdcruz@ufv.br, marciane.silva.oliveira@gmail.comUniversidade Federal de ViçosaBrazilViçosa, MG, Brazil Universidade Federal de Viçosa, Departamento de Biologia Geral, Avenida Peter Henry Rolfs, s/no, Campus Universitário, CEP 36570-000 Viçosa, MG, Brazil. E-mail: michelejorgesilva@gmail.com, antonio.silva.c.junior@gmail.com, cdcruz@ufv.br, marciane.silva.oliveira@gmail.com

http://orcid.org/0000-0001-8648-8825

Antônio Carlos da Silva Júnior

http://orcid.org/0000-0001-9911-6553

Cosme Damião Cruz

http://orcid.org/0000-0003-3513-3391

Moysés Nascimento

Universidade Federal de Viçosa, Departamento de Estatística, Avenida Peter Henry Rolfs, s/no, Campus Universitário, CEP 36570-977 Viçosa, MG, Brazil. E-mail: moysesnascim@ufv.brUniversidade Federal de ViçosaBrazilViçosa, MG, Brazil Universidade Federal de Viçosa, Departamento de Estatística, Avenida Peter Henry Rolfs, s/no, Campus Universitário, CEP 36570-977 Viçosa, MG, Brazil. E-mail: moysesnascim@ufv.br

http://orcid.org/0000-0001-5886-9540

Marciane da Silva Oliveira

http://orcid.org/0000-0002-9504-4115

Robert Eugene Schaffert

Embrapa Milho e Sorgo, Rodovia MG-424, Km 45, Caixa Postal 285, CEP 35701-970 Sete Lagoas, MG, Brazil. E-mail: robert.schaffert@embrapa.br, rafael.parrella@embrapa.brEmbrapa Milho e SorgoBrazilSete Lagoas, MG, Brazil Embrapa Milho e Sorgo, Rodovia MG-424, Km 45, Caixa Postal 285, CEP 35701-970 Sete Lagoas, MG, Brazil. E-mail: robert.schaffert@embrapa.br, rafael.parrella@embrapa.br

http://orcid.org/0000-0002-9388-8031

Rafael Augusto da Costa Parrella

http://orcid.org/0000-0001-6599-7487

*Corresponding author: michelejorgesilva@gmail.com

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (2)
Tables (4)
Formulas (1)

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Figure 1.
Graphical dispersion of biomass sorghum (Sorghum bicolor) lines based on the first two canonical variables (CV1 and CV2), which were obtained through the analysis of five traits evaluated in Nova Porteirinha (NP) and Sete Lagoas (SL), in the state of Minas Gerais, Brazil.

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Figure 2.
Arrangement of the clustering scenarios, using five columns and five rows for four experiments, according to the self-organizing map (SOM) for Nova Porteirinha (NP) and Sete Lagoas (SL), in the state of Minas Gerais, Brazil.

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Table 1.
Biomass sorghum (Sorghum bicolor) parents and hybrids used in the partial diallel in experiments I, II, III and IV⁽¹⁾.

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Table 2.
Summary of the joint analysis of variance for days to flowering (FLOW), plant height (PH), fresh biomass yield (FBY), total dry biomass (DB), and dry biomass yield (DBY) for the hybrids, parents, and controls of biomass sorghum (Sorghum bicolor), in the 2016/2017 and 2017/2018 crop years, in the municipalities of Nova Porteirinha and Sete Lagoas, in the state of Minas Gerais, Brazil.

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Table 3.
Estimates of variance (eigenvalues) associated with canonical variables, related to five traits evaluated in biomass sorghum (Sorghum bicolor) in the municipalities Nova Porteirinha (NP) and Sete Lagoas (SL), in the state of Minas Gerais, Brazil.

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Table 4.
Organization of genotypes in neurons through the self-organizing map (SOM) for Nova Porteirinha (NP) and Sete Lagoas (SL) in the 2016/2017 and 2017/2018 crop years, in the state of Minas Gerais, Brazil.

Thumbnail

Figure 1. Graphical dispersion of biomass sorghum (Sorghum bicolor) lines based on the first two canonical variables (CV1 and CV2), which were obtained through the analysis of five traits evaluated in Nova Porteirinha (NP) and Sete Lagoas (SL), in the state of Minas Gerais, Brazil.

Figure 2. Arrangement of the clustering scenarios, using five columns and five rows for four experiments, according to the self-organizing map (SOM) for Nova Porteirinha (NP) and Sete Lagoas (SL), in the state of Minas Gerais, Brazil.

Table 1. Biomass sorghum (Sorghum bicolor) parents and hybrids used in the partial diallel in experiments I, II, III and IV⁽¹⁾.

Group II (R line)	Group I (A line)
Group II (R line)	BR007A bmr (1)	CMSXS156A bmr (2)	CMSXS157A bmr (3)	TX635Abmr(4)
	Experiments I and II
201635B004 bmr (1)	H_(1-1)	H_(2-1)	H_(3-1)	-
201635B005 bmr (2)	H_(1-2)	H_(2-2)	H_(3-2)	-
201635B006 bmr (3)	H_(1-3)	H_(2-3)	H_(3-3)	-
201635B007 bmr (4)	H_(1-4)	H_(2-4)	H_(3-4)	-
201635B008 bmr (5)	H_(1-5)	H_(2-5)	H_(3-5)	-
201635B009 bmr (6)	H_(1-6)	H_(2-6)	H_(3-6)	-
201635B010 bmr (7)	H_(1-7)	H_(2-7)	H_(3-7)	-
201635B011 bmr (8)	H_(1-8)	H_(2-8)	H_(3-8)	-
201635B012 bmr (9)	H_(1-9)	H_(2-9)	H_(3-9)	-
201635B013 bmr (10)	H_(1-10)	H_(2-10)	H_(3-10)	-
	Experiments III and IV
201635B004 bmr (1)	H_(1-1)	H_(2-1)	H_(3-1)	H_(4-1)
201635B005 bmr (2)	H_(1-2)	H_(2-2)	H_(3-2)	H_(4-2)
201635B006 bmr (3)	H_(1-3)	H_(2-3)	H_(3-3)	H_(4-3)
201635B007 bmr (4)	H_(1-4)	H_(2-4)	H_(3-4)	H_(4-4)
201635B008 bmr (5)	H_(1-5)	H_(2-5)	H_(3-5)	H_(4-5)
201635B009 bmr (6)	H_(1-6)	H_(2-6)	H_(3-6)	H_(4-6)
201635B010 bmr (7)	H_(1-7)	H_(2-7)	H_(3-7)	H_(4-7)
201635B011 bmr (8)	H_(1-8)	H_(2-8)	H_(3-8)	H_(4-8)
201635B012 bmr (9)	H_(1-9)	H_(2-9)	H_(3-9)	H_(4-9)
201635B013 bmr (10)	H_(1-10)	H_(2-10)	H_(3-10)	H_(4-10)

⁽¹⁾Values in parentheses refer to the 4 lines of group I, 10 lines of group II, and the 40 hybrids derived from the crosses between these lines for the experiments I and II, as well as to the 4 lines of group I, 10 lines of group II, and 40 hybrids from crosses between these lines for the experiments III and IV.

Table 2. Summary of the joint analysis of variance for days to flowering (FLOW), plant height (PH), fresh biomass yield (FBY), total dry biomass (DB), and dry biomass yield (DBY) for the hybrids, parents, and controls of biomass sorghum (Sorghum bicolor), in the 2016/2017 and 2017/2018 crop years, in the municipalities of Nova Porteirinha and Sete Lagoas, in the state of Minas Gerais, Brazil.

Source of variation	Degree of freedom	Mean squares
Source of variation	Degree of freedom	FLOW	PH	FBY	DB	DBY
		2016/2017 crop year
Genotype (G)	43	3,085.41**	4.49**	4,241.95**	227.26**	304.36*
Environment (E)	1	3,354.09^ns	41.68**	36,859.01^ns	2,877.84^ns	3,940.75^ns
G x E	43	772.88**	0.32**	1,000.94**	1,000.19**	163.62**
Mean		131.68	4.10	100.74	31.96	36.30
Coefficient of variation (%)		3.86	5.14	6.88	8.09	6.54
		2017/2018 crop year
Genotype (G)	43	1,662.69**	5.15**	3,797.85**	147.89^ns	146.67**
Environment (E)	1	2,310.45^ns	3.18^ns	2,583.00^ns	2,498.49^ns	796.78^ns
G x E	43	466.79**	0.13**	1,085.58**	106.65**	80.37**
Mean		131.43	4.15	83.34	26.92	26.0
Coefficient of variation (%)		4.52	5.57	5.28	7.93	6.38

**, *Significant at 1% and 5% probability, by the F test. ^nsNonsignificant.

Table 3. Estimates of variance (eigenvalues) associated with canonical variables, related to five traits evaluated in biomass sorghum (Sorghum bicolor) in the municipalities Nova Porteirinha (NP) and Sete Lagoas (SL), in the state of Minas Gerais, Brazil.

Canonical variable accumulated (%)
NP (2016/2017)		SL (2016/2017)
CV1	79.45	CV1	90.00
CV2	92.94	CV2	97.45
CV3	98.93	CV3	98.84
CV4	99.75	CV4	99.47
CV5	100.0	CV5	100.0
NP (2017/2018)		SL (2017/2018)
CV1	74.49	CV1	72.48
CV2	89.53	CV2	84.64
CV3	94.36	CV3	94.71
CV4	97.88	CV4	98.81
CV5	100.0	CV5	100.0

CV, coefficient of variation.

Table 4. Organization of genotypes in neurons through the self-organizing map (SOM) for Nova Porteirinha (NP) and Sete Lagoas (SL) in the 2016/2017 and 2017/2018 crop years, in the state of Minas Gerais, Brazil.

Neuron	2016/2017 crop year		2017/2018 crop year
Neuron	Nova Porteirinha (NP)	Sete Lagoas (SL)	Nova Porteirinha (NP)	Sete Lagoas (SL)
1	44, 47, 48	7, 8, 27, 28, 31, 35	18, 23, 56	18, 19, 56
2	25	39	48, 51	17, 24
3	27, 31, 36, 37, 41	22, 36	22, 38, 39, 40, 41	20
4		6, 14, 30	34	16, 30, 49
5		11, 13, 21	20, 47, 49	47
6	46, 49	19, 41	19, 44, 54	21
7	16, 26	37	15	6, 28, 53
8	5, 14, 22, 38,	4, 32	8, 27, 29, 31, 50
9	19, 29, 40		45
10	1, 2, 3	12	30	1, 2, 3, 4
11	15, 45	24	36	32, 36
12	17, 18	42	17, 24, 26	40, 43, 52, 54
13	20, 35	9, 29	9, 21, 42	22, 23, 39
14		40	35, 46, 52	12, 33, 34
15		33, 34, 43	18	55
16		25, 38, 47	14	15, 37, 42
17	6, 9, 34, 39	16, 26, 49	5, 6, 7, 11, 13	5, 51
18	24, 32, 33	15, 20, 23	12, 25	29, 31, 41
19			16	7, 27
20	13	1, 2, 3	1, 2, 3, 4	10, 25, 45
21	7, 8, 10, 21, 23	44	10, 32, 37, 43, 53	38, 48, 50
22	28	18, 48		26, 46
23		17	33	8, 9, 13, 14
24	11, 30, 42	10	55	11
25	4	5		35, 44

y_{i j k} = μ + g_{i} + e_{j} + g e_{i j} + b / e_{j k} + ε_{i j k}

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Computational intelligence for studies on genetic diversity between genotypes of biomass sorghum

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[1] *Corresponding author: michelejorgesilva@gmail.com